OpenBLAS/lapack-netlib/SRC/zggev3.c

#include <math.h>
#include <stdlib.h>
#include <string.h>
#include <stdio.h>
#include <complex.h>
#ifdef complex
#undef complex
#endif
#ifdef I
#undef I
#endif

#if defined(_WIN64)
typedef long long BLASLONG;
typedef unsigned long long BLASULONG;
#else
typedef long BLASLONG;
typedef unsigned long BLASULONG;
#endif

#ifdef LAPACK_ILP64
typedef BLASLONG blasint;
#if defined(_WIN64)
#define blasabs(x) llabs(x)
#else
#define blasabs(x) labs(x)
#endif
#else
typedef int blasint;
#define blasabs(x) abs(x)
#endif

typedef blasint integer;

typedef unsigned int uinteger;
typedef char *address;
typedef short int shortint;
typedef float real;
typedef double doublereal;
typedef struct { real r, i; } complex;
typedef struct { doublereal r, i; } doublecomplex;
#ifdef _MSC_VER
static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}
static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}
static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}
static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}
#else
static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}
static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}
static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}
static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}
#endif
#define pCf(z) (*_pCf(z))
#define pCd(z) (*_pCd(z))
typedef int logical;
typedef short int shortlogical;
typedef char logical1;
typedef char integer1;

#define TRUE_ (1)
#define FALSE_ (0)

/* Extern is for use with -E */
#ifndef Extern
#define Extern extern
#endif

/* I/O stuff */

typedef int flag;
typedef int ftnlen;
typedef int ftnint;

/*external read, write*/
typedef struct
{	flag cierr;
	ftnint ciunit;
	flag ciend;
	char *cifmt;
	ftnint cirec;
} cilist;

/*internal read, write*/
typedef struct
{	flag icierr;
	char *iciunit;
	flag iciend;
	char *icifmt;
	ftnint icirlen;
	ftnint icirnum;
} icilist;

/*open*/
typedef struct
{	flag oerr;
	ftnint ounit;
	char *ofnm;
	ftnlen ofnmlen;
	char *osta;
	char *oacc;
	char *ofm;
	ftnint orl;
	char *oblnk;
} olist;

/*close*/
typedef struct
{	flag cerr;
	ftnint cunit;
	char *csta;
} cllist;

/*rewind, backspace, endfile*/
typedef struct
{	flag aerr;
	ftnint aunit;
} alist;

/* inquire */
typedef struct
{	flag inerr;
	ftnint inunit;
	char *infile;
	ftnlen infilen;
	ftnint	*inex;	/*parameters in standard's order*/
	ftnint	*inopen;
	ftnint	*innum;
	ftnint	*innamed;
	char	*inname;
	ftnlen	innamlen;
	char	*inacc;
	ftnlen	inacclen;
	char	*inseq;
	ftnlen	inseqlen;
	char 	*indir;
	ftnlen	indirlen;
	char	*infmt;
	ftnlen	infmtlen;
	char	*inform;
	ftnint	informlen;
	char	*inunf;
	ftnlen	inunflen;
	ftnint	*inrecl;
	ftnint	*innrec;
	char	*inblank;
	ftnlen	inblanklen;
} inlist;

#define VOID void

union Multitype {	/* for multiple entry points */
	integer1 g;
	shortint h;
	integer i;
	/* longint j; */
	real r;
	doublereal d;
	complex c;
	doublecomplex z;
	};

typedef union Multitype Multitype;

struct Vardesc {	/* for Namelist */
	char *name;
	char *addr;
	ftnlen *dims;
	int  type;
	};
typedef struct Vardesc Vardesc;

struct Namelist {
	char *name;
	Vardesc **vars;
	int nvars;
	};
typedef struct Namelist Namelist;

#define abs(x) ((x) >= 0 ? (x) : -(x))
#define dabs(x) (fabs(x))
#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))
#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))
#define dmin(a,b) (f2cmin(a,b))
#define dmax(a,b) (f2cmax(a,b))
#define bit_test(a,b)	((a) >> (b) & 1)
#define bit_clear(a,b)	((a) & ~((uinteger)1 << (b)))
#define bit_set(a,b)	((a) |  ((uinteger)1 << (b)))

#define abort_() { sig_die("Fortran abort routine called", 1); }
#define c_abs(z) (cabsf(Cf(z)))
#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }
#ifdef _MSC_VER
#define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}
#define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/df(b)._Val[1]);}
#else
#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}
#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}
#endif
#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}
#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}
#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}
//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}
#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}
#define d_abs(x) (fabs(*(x)))
#define d_acos(x) (acos(*(x)))
#define d_asin(x) (asin(*(x)))
#define d_atan(x) (atan(*(x)))
#define d_atn2(x, y) (atan2(*(x),*(y)))
#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }
#define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }
#define d_cos(x) (cos(*(x)))
#define d_cosh(x) (cosh(*(x)))
#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )
#define d_exp(x) (exp(*(x)))
#define d_imag(z) (cimag(Cd(z)))
#define r_imag(z) (cimagf(Cf(z)))
#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))
#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )
#define d_log(x) (log(*(x)))
#define d_mod(x, y) (fmod(*(x), *(y)))
#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))
#define d_nint(x) u_nint(*(x))
#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))
#define d_sign(a,b) u_sign(*(a),*(b))
#define r_sign(a,b) u_sign(*(a),*(b))
#define d_sin(x) (sin(*(x)))
#define d_sinh(x) (sinh(*(x)))
#define d_sqrt(x) (sqrt(*(x)))
#define d_tan(x) (tan(*(x)))
#define d_tanh(x) (tanh(*(x)))
#define i_abs(x) abs(*(x))
#define i_dnnt(x) ((integer)u_nint(*(x)))
#define i_len(s, n) (n)
#define i_nint(x) ((integer)u_nint(*(x)))
#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))
#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))
#define pow_si(B,E) spow_ui(*(B),*(E))
#define pow_ri(B,E) spow_ui(*(B),*(E))
#define pow_di(B,E) dpow_ui(*(B),*(E))
#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}
#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}
#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}
#define s_cat(lpp, rpp, rnp, np, llp) { 	ftnlen i, nc, ll; char *f__rp, *lp; 	ll = (llp); lp = (lpp); 	for(i=0; i < (int)*(np); ++i) {         	nc = ll; 	        if((rnp)[i] < nc) nc = (rnp)[i]; 	        ll -= nc;         	f__rp = (rpp)[i]; 	        while(--nc >= 0) *lp++ = *(f__rp)++;         } 	while(--ll >= 0) *lp++ = ' '; }
#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))
#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }
#define sig_die(s, kill) { exit(1); }
#define s_stop(s, n) {exit(0);}
static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";
#define z_abs(z) (cabs(Cd(z)))
#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}
#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}
#define myexit_() break;
#define mycycle() continue;
#define myceiling(w) {ceil(w)}
#define myhuge(w) {HUGE_VAL}
//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}
#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}

/* procedure parameter types for -A and -C++ */

#define F2C_proc_par_types 1
#ifdef __cplusplus
typedef logical (*L_fp)(...);
#else
typedef logical (*L_fp)();
#endif

static float spow_ui(float x, integer n) {
	float pow=1.0; unsigned long int u;
	if(n != 0) {
		if(n < 0) n = -n, x = 1/x;
		for(u = n; ; ) {
			if(u & 01) pow *= x;
			if(u >>= 1) x *= x;
			else break;
		}
	}
	return pow;
}
static double dpow_ui(double x, integer n) {
	double pow=1.0; unsigned long int u;
	if(n != 0) {
		if(n < 0) n = -n, x = 1/x;
		for(u = n; ; ) {
			if(u & 01) pow *= x;
			if(u >>= 1) x *= x;
			else break;
		}
	}
	return pow;
}
#ifdef _MSC_VER
static _Fcomplex cpow_ui(complex x, integer n) {
	complex pow={1.0,0.0}; unsigned long int u;
		if(n != 0) {
		if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;
		for(u = n; ; ) {
			if(u & 01) pow.r *= x.r, pow.i *= x.i;
			if(u >>= 1) x.r *= x.r, x.i *= x.i;
			else break;
		}
	}
	_Fcomplex p={pow.r, pow.i};
	return p;
}
#else
static _Complex float cpow_ui(_Complex float x, integer n) {
	_Complex float pow=1.0; unsigned long int u;
	if(n != 0) {
		if(n < 0) n = -n, x = 1/x;
		for(u = n; ; ) {
			if(u & 01) pow *= x;
			if(u >>= 1) x *= x;
			else break;
		}
	}
	return pow;
}
#endif
#ifdef _MSC_VER
static _Dcomplex zpow_ui(_Dcomplex x, integer n) {
	_Dcomplex pow={1.0,0.0}; unsigned long int u;
	if(n != 0) {
		if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];
		for(u = n; ; ) {
			if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];
			if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];
			else break;
		}
	}
	_Dcomplex p = {pow._Val[0], pow._Val[1]};
	return p;
}
#else
static _Complex double zpow_ui(_Complex double x, integer n) {
	_Complex double pow=1.0; unsigned long int u;
	if(n != 0) {
		if(n < 0) n = -n, x = 1/x;
		for(u = n; ; ) {
			if(u & 01) pow *= x;
			if(u >>= 1) x *= x;
			else break;
		}
	}
	return pow;
}
#endif
static integer pow_ii(integer x, integer n) {
	integer pow; unsigned long int u;
	if (n <= 0) {
		if (n == 0 || x == 1) pow = 1;
		else if (x != -1) pow = x == 0 ? 1/x : 0;
		else n = -n;
	}
	if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {
		u = n;
		for(pow = 1; ; ) {
			if(u & 01) pow *= x;
			if(u >>= 1) x *= x;
			else break;
		}
	}
	return pow;
}
static integer dmaxloc_(double *w, integer s, integer e, integer *n)
{
	double m; integer i, mi;
	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
		if (w[i-1]>m) mi=i ,m=w[i-1];
	return mi-s+1;
}
static integer smaxloc_(float *w, integer s, integer e, integer *n)
{
	float m; integer i, mi;
	for(m=w[s-1], mi=s, i=s+1; i<=e; i++)
		if (w[i-1]>m) mi=i ,m=w[i-1];
	return mi-s+1;
}
static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
	integer n = *n_, incx = *incx_, incy = *incy_, i;
#ifdef _MSC_VER
	_Fcomplex zdotc = {0.0, 0.0};
	if (incx == 1 && incy == 1) {
		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
			zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];
			zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];
		}
	} else {
		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
			zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];
			zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];
		}
	}
	pCf(z) = zdotc;
}
#else
	_Complex float zdotc = 0.0;
	if (incx == 1 && incy == 1) {
		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
			zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);
		}
	} else {
		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
			zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);
		}
	}
	pCf(z) = zdotc;
}
#endif
static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
	integer n = *n_, incx = *incx_, incy = *incy_, i;
#ifdef _MSC_VER
	_Dcomplex zdotc = {0.0, 0.0};
	if (incx == 1 && incy == 1) {
		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
			zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];
			zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];
		}
	} else {
		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
			zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];
			zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];
		}
	}
	pCd(z) = zdotc;
}
#else
	_Complex double zdotc = 0.0;
	if (incx == 1 && incy == 1) {
		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
			zdotc += conj(Cd(&x[i])) * Cd(&y[i]);
		}
	} else {
		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
			zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);
		}
	}
	pCd(z) = zdotc;
}
#endif	
static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {
	integer n = *n_, incx = *incx_, incy = *incy_, i;
#ifdef _MSC_VER
	_Fcomplex zdotc = {0.0, 0.0};
	if (incx == 1 && incy == 1) {
		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
			zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];
			zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];
		}
	} else {
		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
			zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];
			zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];
		}
	}
	pCf(z) = zdotc;
}
#else
	_Complex float zdotc = 0.0;
	if (incx == 1 && incy == 1) {
		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
			zdotc += Cf(&x[i]) * Cf(&y[i]);
		}
	} else {
		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
			zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);
		}
	}
	pCf(z) = zdotc;
}
#endif
static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {
	integer n = *n_, incx = *incx_, incy = *incy_, i;
#ifdef _MSC_VER
	_Dcomplex zdotc = {0.0, 0.0};
	if (incx == 1 && incy == 1) {
		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
			zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];
			zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];
		}
	} else {
		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
			zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];
			zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];
		}
	}
	pCd(z) = zdotc;
}
#else
	_Complex double zdotc = 0.0;
	if (incx == 1 && incy == 1) {
		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
			zdotc += Cd(&x[i]) * Cd(&y[i]);
		}
	} else {
		for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */
			zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);
		}
	}
	pCd(z) = zdotc;
}
#endif
/*  -- translated by f2c (version 20000121).
   You must link the resulting object file with the libraries:
	-lf2c -lm   (in that order)
*/




/* Table of constant values */

static doublecomplex c_b1 = {0.,0.};
static doublecomplex c_b2 = {1.,0.};
static integer c_n1 = -1;
static integer c__1 = 1;
static integer c__0 = 0;

/* > \brief <b> ZGGEV3 computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE mat
rices (blocked algorithm)</b> */

/*  =========== DOCUMENTATION =========== */

/* Online html documentation available at */
/*            http://www.netlib.org/lapack/explore-html/ */

/* > \htmlonly */
/* > Download ZGGEV3 + dependencies */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zggev3.
f"> */
/* > [TGZ]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zggev3.
f"> */
/* > [ZIP]</a> */
/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zggev3.
f"> */
/* > [TXT]</a> */
/* > \endhtmlonly */

/*  Definition: */
/*  =========== */

/*       SUBROUTINE ZGGEV3( JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHA, BETA, */
/*                          VL, LDVL, VR, LDVR, WORK, LWORK, RWORK, INFO ) */

/*       CHARACTER          JOBVL, JOBVR */
/*       INTEGER            INFO, LDA, LDB, LDVL, LDVR, LWORK, N */
/*       DOUBLE PRECISION   RWORK( * ) */
/*       COMPLEX*16         A( LDA, * ), ALPHA( * ), B( LDB, * ), */
/*      $                   BETA( * ), VL( LDVL, * ), VR( LDVR, * ), */
/*      $                   WORK( * ) */


/* > \par Purpose: */
/*  ============= */
/* > */
/* > \verbatim */
/* > */
/* > ZGGEV3 computes for a pair of N-by-N complex nonsymmetric matrices */
/* > (A,B), the generalized eigenvalues, and optionally, the left and/or */
/* > right generalized eigenvectors. */
/* > */
/* > A generalized eigenvalue for a pair of matrices (A,B) is a scalar */
/* > lambda or a ratio alpha/beta = lambda, such that A - lambda*B is */
/* > singular. It is usually represented as the pair (alpha,beta), as */
/* > there is a reasonable interpretation for beta=0, and even for both */
/* > being zero. */
/* > */
/* > The right generalized eigenvector v(j) corresponding to the */
/* > generalized eigenvalue lambda(j) of (A,B) satisfies */
/* > */
/* >              A * v(j) = lambda(j) * B * v(j). */
/* > */
/* > The left generalized eigenvector u(j) corresponding to the */
/* > generalized eigenvalues lambda(j) of (A,B) satisfies */
/* > */
/* >              u(j)**H * A = lambda(j) * u(j)**H * B */
/* > */
/* > where u(j)**H is the conjugate-transpose of u(j). */
/* > \endverbatim */

/*  Arguments: */
/*  ========== */

/* > \param[in] JOBVL */
/* > \verbatim */
/* >          JOBVL is CHARACTER*1 */
/* >          = 'N':  do not compute the left generalized eigenvectors; */
/* >          = 'V':  compute the left generalized eigenvectors. */
/* > \endverbatim */
/* > */
/* > \param[in] JOBVR */
/* > \verbatim */
/* >          JOBVR is CHARACTER*1 */
/* >          = 'N':  do not compute the right generalized eigenvectors; */
/* >          = 'V':  compute the right generalized eigenvectors. */
/* > \endverbatim */
/* > */
/* > \param[in] N */
/* > \verbatim */
/* >          N is INTEGER */
/* >          The order of the matrices A, B, VL, and VR.  N >= 0. */
/* > \endverbatim */
/* > */
/* > \param[in,out] A */
/* > \verbatim */
/* >          A is COMPLEX*16 array, dimension (LDA, N) */
/* >          On entry, the matrix A in the pair (A,B). */
/* >          On exit, A has been overwritten. */
/* > \endverbatim */
/* > */
/* > \param[in] LDA */
/* > \verbatim */
/* >          LDA is INTEGER */
/* >          The leading dimension of A.  LDA >= f2cmax(1,N). */
/* > \endverbatim */
/* > */
/* > \param[in,out] B */
/* > \verbatim */
/* >          B is COMPLEX*16 array, dimension (LDB, N) */
/* >          On entry, the matrix B in the pair (A,B). */
/* >          On exit, B has been overwritten. */
/* > \endverbatim */
/* > */
/* > \param[in] LDB */
/* > \verbatim */
/* >          LDB is INTEGER */
/* >          The leading dimension of B.  LDB >= f2cmax(1,N). */
/* > \endverbatim */
/* > */
/* > \param[out] ALPHA */
/* > \verbatim */
/* >          ALPHA is COMPLEX*16 array, dimension (N) */
/* > \endverbatim */
/* > */
/* > \param[out] BETA */
/* > \verbatim */
/* >          BETA is COMPLEX*16 array, dimension (N) */
/* >          On exit, ALPHA(j)/BETA(j), j=1,...,N, will be the */
/* >          generalized eigenvalues. */
/* > */
/* >          Note: the quotients ALPHA(j)/BETA(j) may easily over- or */
/* >          underflow, and BETA(j) may even be zero.  Thus, the user */
/* >          should avoid naively computing the ratio alpha/beta. */
/* >          However, ALPHA will be always less than and usually */
/* >          comparable with norm(A) in magnitude, and BETA always less */
/* >          than and usually comparable with norm(B). */
/* > \endverbatim */
/* > */
/* > \param[out] VL */
/* > \verbatim */
/* >          VL is COMPLEX*16 array, dimension (LDVL,N) */
/* >          If JOBVL = 'V', the left generalized eigenvectors u(j) are */
/* >          stored one after another in the columns of VL, in the same */
/* >          order as their eigenvalues. */
/* >          Each eigenvector is scaled so the largest component has */
/* >          abs(real part) + abs(imag. part) = 1. */
/* >          Not referenced if JOBVL = 'N'. */
/* > \endverbatim */
/* > */
/* > \param[in] LDVL */
/* > \verbatim */
/* >          LDVL is INTEGER */
/* >          The leading dimension of the matrix VL. LDVL >= 1, and */
/* >          if JOBVL = 'V', LDVL >= N. */
/* > \endverbatim */
/* > */
/* > \param[out] VR */
/* > \verbatim */
/* >          VR is COMPLEX*16 array, dimension (LDVR,N) */
/* >          If JOBVR = 'V', the right generalized eigenvectors v(j) are */
/* >          stored one after another in the columns of VR, in the same */
/* >          order as their eigenvalues. */
/* >          Each eigenvector is scaled so the largest component has */
/* >          abs(real part) + abs(imag. part) = 1. */
/* >          Not referenced if JOBVR = 'N'. */
/* > \endverbatim */
/* > */
/* > \param[in] LDVR */
/* > \verbatim */
/* >          LDVR is INTEGER */
/* >          The leading dimension of the matrix VR. LDVR >= 1, and */
/* >          if JOBVR = 'V', LDVR >= N. */
/* > \endverbatim */
/* > */
/* > \param[out] WORK */
/* > \verbatim */
/* >          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK)) */
/* >          On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */
/* > \endverbatim */
/* > */
/* > \param[in] LWORK */
/* > \verbatim */
/* >          LWORK is INTEGER */
/* >          The dimension of the array WORK. */
/* > */
/* >          If LWORK = -1, then a workspace query is assumed; the routine */
/* >          only calculates the optimal size of the WORK array, returns */
/* >          this value as the first entry of the WORK array, and no error */
/* >          message related to LWORK is issued by XERBLA. */
/* > \endverbatim */
/* > */
/* > \param[out] RWORK */
/* > \verbatim */
/* >          RWORK is DOUBLE PRECISION array, dimension (8*N) */
/* > \endverbatim */
/* > */
/* > \param[out] INFO */
/* > \verbatim */
/* >          INFO is INTEGER */
/* >          = 0:  successful exit */
/* >          < 0:  if INFO = -i, the i-th argument had an illegal value. */
/* >          =1,...,N: */
/* >                The QZ iteration failed.  No eigenvectors have been */
/* >                calculated, but ALPHA(j) and BETA(j) should be */
/* >                correct for j=INFO+1,...,N. */
/* >          > N:  =N+1: other then QZ iteration failed in DHGEQZ, */
/* >                =N+2: error return from DTGEVC. */
/* > \endverbatim */

/*  Authors: */
/*  ======== */

/* > \author Univ. of Tennessee */
/* > \author Univ. of California Berkeley */
/* > \author Univ. of Colorado Denver */
/* > \author NAG Ltd. */

/* > \date January 2015 */

/* > \ingroup complex16GEeigen */

/*  ===================================================================== */
/* Subroutine */ void zggev3_(char *jobvl, char *jobvr, integer *n, 
	doublecomplex *a, integer *lda, doublecomplex *b, integer *ldb, 
	doublecomplex *alpha, doublecomplex *beta, doublecomplex *vl, integer 
	*ldvl, doublecomplex *vr, integer *ldvr, doublecomplex *work, integer 
	*lwork, doublereal *rwork, integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, b_dim1, b_offset, vl_dim1, vl_offset, vr_dim1, 
	    vr_offset, i__1, i__2, i__3, i__4;
    doublereal d__1, d__2, d__3, d__4;
    doublecomplex z__1;

    /* Local variables */
    doublereal anrm, bnrm;
    integer ierr, itau;
    doublereal temp;
    logical ilvl, ilvr;
    integer iwrk;
    extern logical lsame_(char *, char *);
    integer ileft, icols, irwrk, irows;
    extern /* Subroutine */ void zgghd3_(char *, char *, integer *, integer *, 
	    integer *, doublecomplex *, integer *, doublecomplex *, integer *,
	     doublecomplex *, integer *, doublecomplex *, integer *, 
	    doublecomplex *, integer *, integer *), dlabad_(
	    doublereal *, doublereal *);
    integer jc, in;
    extern doublereal dlamch_(char *);
    integer jr;
    extern /* Subroutine */ void zggbak_(char *, char *, integer *, integer *, 
	    integer *, doublereal *, doublereal *, integer *, doublecomplex *,
	     integer *, integer *), zggbal_(char *, integer *,
	     doublecomplex *, integer *, doublecomplex *, integer *, integer *
	    , integer *, doublereal *, doublereal *, doublereal *, integer *);
    logical ilascl, ilbscl;
    extern /* Subroutine */ int xerbla_(char *, integer *, ftnlen);
    logical ldumma[1];
    char chtemp[1];
    doublereal bignum;
    extern doublereal zlange_(char *, integer *, integer *, doublecomplex *, 
	    integer *, doublereal *);
    integer ijobvl, iright;
    extern /* Subroutine */ void zlascl_(char *, integer *, integer *, 
	    doublereal *, doublereal *, integer *, integer *, doublecomplex *,
	     integer *, integer *);
    integer ijobvr;
    extern /* Subroutine */ void zgeqrf_(integer *, integer *, doublecomplex *,
	     integer *, doublecomplex *, doublecomplex *, integer *, integer *
	    );
    doublereal anrmto, bnrmto;
    extern /* Subroutine */ void zlacpy_(char *, integer *, integer *, 
	    doublecomplex *, integer *, doublecomplex *, integer *), 
	    zlaset_(char *, integer *, integer *, doublecomplex *, 
	    doublecomplex *, doublecomplex *, integer *), ztgevc_(
	    char *, char *, logical *, integer *, doublecomplex *, integer *, 
	    doublecomplex *, integer *, doublecomplex *, integer *, 
	    doublecomplex *, integer *, integer *, integer *, doublecomplex *,
	     doublereal *, integer *), zhgeqz_(char *, char *,
	     char *, integer *, integer *, integer *, doublecomplex *, 
	    integer *, doublecomplex *, integer *, doublecomplex *, 
	    doublecomplex *, doublecomplex *, integer *, doublecomplex *, 
	    integer *, doublecomplex *, integer *, doublereal *, integer *);
    doublereal smlnum;
    integer lwkopt;
    logical lquery;
    extern /* Subroutine */ void zungqr_(integer *, integer *, integer *, 
	    doublecomplex *, integer *, doublecomplex *, doublecomplex *, 
	    integer *, integer *), zunmqr_(char *, char *, integer *, integer 
	    *, integer *, doublecomplex *, integer *, doublecomplex *, 
	    doublecomplex *, integer *, doublecomplex *, integer *, integer *);
    integer ihi, ilo;
    doublereal eps;
    logical ilv;


/*  -- LAPACK driver routine (version 3.6.1) -- */
/*  -- LAPACK is a software package provided by Univ. of Tennessee,    -- */
/*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
/*     January 2015 */


/*  ===================================================================== */


/*     Decode the input arguments */

    /* Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1 * 1;
    a -= a_offset;
    b_dim1 = *ldb;
    b_offset = 1 + b_dim1 * 1;
    b -= b_offset;
    --alpha;
    --beta;
    vl_dim1 = *ldvl;
    vl_offset = 1 + vl_dim1 * 1;
    vl -= vl_offset;
    vr_dim1 = *ldvr;
    vr_offset = 1 + vr_dim1 * 1;
    vr -= vr_offset;
    --work;
    --rwork;

    /* Function Body */
    if (lsame_(jobvl, "N")) {
	ijobvl = 1;
	ilvl = FALSE_;
    } else if (lsame_(jobvl, "V")) {
	ijobvl = 2;
	ilvl = TRUE_;
    } else {
	ijobvl = -1;
	ilvl = FALSE_;
    }

    if (lsame_(jobvr, "N")) {
	ijobvr = 1;
	ilvr = FALSE_;
    } else if (lsame_(jobvr, "V")) {
	ijobvr = 2;
	ilvr = TRUE_;
    } else {
	ijobvr = -1;
	ilvr = FALSE_;
    }
    ilv = ilvl || ilvr;

/*     Test the input arguments */

    *info = 0;
    lquery = *lwork == -1;
    if (ijobvl <= 0) {
	*info = -1;
    } else if (ijobvr <= 0) {
	*info = -2;
    } else if (*n < 0) {
	*info = -3;
    } else if (*lda < f2cmax(1,*n)) {
	*info = -5;
    } else if (*ldb < f2cmax(1,*n)) {
	*info = -7;
    } else if (*ldvl < 1 || ilvl && *ldvl < *n) {
	*info = -11;
    } else if (*ldvr < 1 || ilvr && *ldvr < *n) {
	*info = -13;
    } else /* if(complicated condition) */ {
/* Computing MAX */
	i__1 = 1, i__2 = *n << 1;
	if (*lwork < f2cmax(i__1,i__2) && ! lquery) {
	    *info = -15;
	}
    }

/*     Compute workspace */

    if (*info == 0) {
	zgeqrf_(n, n, &b[b_offset], ldb, &work[1], &work[1], &c_n1, &ierr);
/* Computing MAX */
	i__1 = 1, i__2 = *n + (integer) work[1].r;
	lwkopt = f2cmax(i__1,i__2);
	zunmqr_("L", "C", n, n, n, &b[b_offset], ldb, &work[1], &a[a_offset], 
		lda, &work[1], &c_n1, &ierr);
/* Computing MAX */
	i__1 = lwkopt, i__2 = *n + (integer) work[1].r;
	lwkopt = f2cmax(i__1,i__2);
	if (ilvl) {
	    zungqr_(n, n, n, &vl[vl_offset], ldvl, &work[1], &work[1], &c_n1, 
		    &ierr);
/* Computing MAX */
	    i__1 = lwkopt, i__2 = *n + (integer) work[1].r;
	    lwkopt = f2cmax(i__1,i__2);
	}
	if (ilv) {
	    zgghd3_(jobvl, jobvr, n, &c__1, n, &a[a_offset], lda, &b[b_offset]
		    , ldb, &vl[vl_offset], ldvl, &vr[vr_offset], ldvr, &work[
		    1], &c_n1, &ierr);
/* Computing MAX */
	    i__1 = lwkopt, i__2 = *n + (integer) work[1].r;
	    lwkopt = f2cmax(i__1,i__2);
	    zhgeqz_("S", jobvl, jobvr, n, &c__1, n, &a[a_offset], lda, &b[
		    b_offset], ldb, &alpha[1], &beta[1], &vl[vl_offset], ldvl,
		     &vr[vr_offset], ldvr, &work[1], &c_n1, &rwork[1], &ierr);
/* Computing MAX */
	    i__1 = lwkopt, i__2 = *n + (integer) work[1].r;
	    lwkopt = f2cmax(i__1,i__2);
	} else {
	    zgghd3_(jobvl, jobvr, n, &c__1, n, &a[a_offset], lda, &b[b_offset]
		    , ldb, &vl[vl_offset], ldvl, &vr[vr_offset], ldvr, &work[
		    1], &c_n1, &ierr);
/* Computing MAX */
	    i__1 = lwkopt, i__2 = *n + (integer) work[1].r;
	    lwkopt = f2cmax(i__1,i__2);
	    zhgeqz_("E", jobvl, jobvr, n, &c__1, n, &a[a_offset], lda, &b[
		    b_offset], ldb, &alpha[1], &beta[1], &vl[vl_offset], ldvl,
		     &vr[vr_offset], ldvr, &work[1], &c_n1, &rwork[1], &ierr);
/* Computing MAX */
	    i__1 = lwkopt, i__2 = *n + (integer) work[1].r;
	    lwkopt = f2cmax(i__1,i__2);
	}
	z__1.r = (doublereal) lwkopt, z__1.i = 0.;
	work[1].r = z__1.r, work[1].i = z__1.i;
    }

    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("ZGGEV3 ", &i__1, (ftnlen)6);
	return;
    } else if (lquery) {
	return;
    }

/*     Quick return if possible */

    if (*n == 0) {
	return;
    }

/*     Get machine constants */

    eps = dlamch_("E") * dlamch_("B");
    smlnum = dlamch_("S");
    bignum = 1. / smlnum;
    dlabad_(&smlnum, &bignum);
    smlnum = sqrt(smlnum) / eps;
    bignum = 1. / smlnum;

/*     Scale A if f2cmax element outside range [SMLNUM,BIGNUM] */

    anrm = zlange_("M", n, n, &a[a_offset], lda, &rwork[1]);
    ilascl = FALSE_;
    if (anrm > 0. && anrm < smlnum) {
	anrmto = smlnum;
	ilascl = TRUE_;
    } else if (anrm > bignum) {
	anrmto = bignum;
	ilascl = TRUE_;
    }
    if (ilascl) {
	zlascl_("G", &c__0, &c__0, &anrm, &anrmto, n, n, &a[a_offset], lda, &
		ierr);
    }

/*     Scale B if f2cmax element outside range [SMLNUM,BIGNUM] */

    bnrm = zlange_("M", n, n, &b[b_offset], ldb, &rwork[1]);
    ilbscl = FALSE_;
    if (bnrm > 0. && bnrm < smlnum) {
	bnrmto = smlnum;
	ilbscl = TRUE_;
    } else if (bnrm > bignum) {
	bnrmto = bignum;
	ilbscl = TRUE_;
    }
    if (ilbscl) {
	zlascl_("G", &c__0, &c__0, &bnrm, &bnrmto, n, n, &b[b_offset], ldb, &
		ierr);
    }

/*     Permute the matrices A, B to isolate eigenvalues if possible */

    ileft = 1;
    iright = *n + 1;
    irwrk = iright + *n;
    zggbal_("P", n, &a[a_offset], lda, &b[b_offset], ldb, &ilo, &ihi, &rwork[
	    ileft], &rwork[iright], &rwork[irwrk], &ierr);

/*     Reduce B to triangular form (QR decomposition of B) */

    irows = ihi + 1 - ilo;
    if (ilv) {
	icols = *n + 1 - ilo;
    } else {
	icols = irows;
    }
    itau = 1;
    iwrk = itau + irows;
    i__1 = *lwork + 1 - iwrk;
    zgeqrf_(&irows, &icols, &b[ilo + ilo * b_dim1], ldb, &work[itau], &work[
	    iwrk], &i__1, &ierr);

/*     Apply the orthogonal transformation to matrix A */

    i__1 = *lwork + 1 - iwrk;
    zunmqr_("L", "C", &irows, &icols, &irows, &b[ilo + ilo * b_dim1], ldb, &
	    work[itau], &a[ilo + ilo * a_dim1], lda, &work[iwrk], &i__1, &
	    ierr);

/*     Initialize VL */

    if (ilvl) {
	zlaset_("Full", n, n, &c_b1, &c_b2, &vl[vl_offset], ldvl);
	if (irows > 1) {
	    i__1 = irows - 1;
	    i__2 = irows - 1;
	    zlacpy_("L", &i__1, &i__2, &b[ilo + 1 + ilo * b_dim1], ldb, &vl[
		    ilo + 1 + ilo * vl_dim1], ldvl);
	}
	i__1 = *lwork + 1 - iwrk;
	zungqr_(&irows, &irows, &irows, &vl[ilo + ilo * vl_dim1], ldvl, &work[
		itau], &work[iwrk], &i__1, &ierr);
    }

/*     Initialize VR */

    if (ilvr) {
	zlaset_("Full", n, n, &c_b1, &c_b2, &vr[vr_offset], ldvr);
    }

/*     Reduce to generalized Hessenberg form */

    if (ilv) {

/*        Eigenvectors requested -- work on whole matrix. */

	i__1 = *lwork + 1 - iwrk;
	zgghd3_(jobvl, jobvr, n, &ilo, &ihi, &a[a_offset], lda, &b[b_offset], 
		ldb, &vl[vl_offset], ldvl, &vr[vr_offset], ldvr, &work[iwrk], 
		&i__1, &ierr);
    } else {
	i__1 = *lwork + 1 - iwrk;
	zgghd3_("N", "N", &irows, &c__1, &irows, &a[ilo + ilo * a_dim1], lda, 
		&b[ilo + ilo * b_dim1], ldb, &vl[vl_offset], ldvl, &vr[
		vr_offset], ldvr, &work[iwrk], &i__1, &ierr);
    }

/*     Perform QZ algorithm (Compute eigenvalues, and optionally, the */
/*     Schur form and Schur vectors) */

    iwrk = itau;
    if (ilv) {
	*(unsigned char *)chtemp = 'S';
    } else {
	*(unsigned char *)chtemp = 'E';
    }
    i__1 = *lwork + 1 - iwrk;
    zhgeqz_(chtemp, jobvl, jobvr, n, &ilo, &ihi, &a[a_offset], lda, &b[
	    b_offset], ldb, &alpha[1], &beta[1], &vl[vl_offset], ldvl, &vr[
	    vr_offset], ldvr, &work[iwrk], &i__1, &rwork[irwrk], &ierr);
    if (ierr != 0) {
	if (ierr > 0 && ierr <= *n) {
	    *info = ierr;
	} else if (ierr > *n && ierr <= *n << 1) {
	    *info = ierr - *n;
	} else {
	    *info = *n + 1;
	}
	goto L70;
    }

/*     Compute Eigenvectors */

    if (ilv) {
	if (ilvl) {
	    if (ilvr) {
		*(unsigned char *)chtemp = 'B';
	    } else {
		*(unsigned char *)chtemp = 'L';
	    }
	} else {
	    *(unsigned char *)chtemp = 'R';
	}

	ztgevc_(chtemp, "B", ldumma, n, &a[a_offset], lda, &b[b_offset], ldb, 
		&vl[vl_offset], ldvl, &vr[vr_offset], ldvr, n, &in, &work[
		iwrk], &rwork[irwrk], &ierr);
	if (ierr != 0) {
	    *info = *n + 2;
	    goto L70;
	}

/*        Undo balancing on VL and VR and normalization */

	if (ilvl) {
	    zggbak_("P", "L", n, &ilo, &ihi, &rwork[ileft], &rwork[iright], n,
		     &vl[vl_offset], ldvl, &ierr);
	    i__1 = *n;
	    for (jc = 1; jc <= i__1; ++jc) {
		temp = 0.;
		i__2 = *n;
		for (jr = 1; jr <= i__2; ++jr) {
/* Computing MAX */
		    i__3 = jr + jc * vl_dim1;
		    d__3 = temp, d__4 = (d__1 = vl[i__3].r, abs(d__1)) + (
			    d__2 = d_imag(&vl[jr + jc * vl_dim1]), abs(d__2));
		    temp = f2cmax(d__3,d__4);
/* L10: */
		}
		if (temp < smlnum) {
		    goto L30;
		}
		temp = 1. / temp;
		i__2 = *n;
		for (jr = 1; jr <= i__2; ++jr) {
		    i__3 = jr + jc * vl_dim1;
		    i__4 = jr + jc * vl_dim1;
		    z__1.r = temp * vl[i__4].r, z__1.i = temp * vl[i__4].i;
		    vl[i__3].r = z__1.r, vl[i__3].i = z__1.i;
/* L20: */
		}
L30:
		;
	    }
	}
	if (ilvr) {
	    zggbak_("P", "R", n, &ilo, &ihi, &rwork[ileft], &rwork[iright], n,
		     &vr[vr_offset], ldvr, &ierr);
	    i__1 = *n;
	    for (jc = 1; jc <= i__1; ++jc) {
		temp = 0.;
		i__2 = *n;
		for (jr = 1; jr <= i__2; ++jr) {
/* Computing MAX */
		    i__3 = jr + jc * vr_dim1;
		    d__3 = temp, d__4 = (d__1 = vr[i__3].r, abs(d__1)) + (
			    d__2 = d_imag(&vr[jr + jc * vr_dim1]), abs(d__2));
		    temp = f2cmax(d__3,d__4);
/* L40: */
		}
		if (temp < smlnum) {
		    goto L60;
		}
		temp = 1. / temp;
		i__2 = *n;
		for (jr = 1; jr <= i__2; ++jr) {
		    i__3 = jr + jc * vr_dim1;
		    i__4 = jr + jc * vr_dim1;
		    z__1.r = temp * vr[i__4].r, z__1.i = temp * vr[i__4].i;
		    vr[i__3].r = z__1.r, vr[i__3].i = z__1.i;
/* L50: */
		}
L60:
		;
	    }
	}
    }

/*     Undo scaling if necessary */

L70:

    if (ilascl) {
	zlascl_("G", &c__0, &c__0, &anrmto, &anrm, n, &c__1, &alpha[1], n, &
		ierr);
    }

    if (ilbscl) {
	zlascl_("G", &c__0, &c__0, &bnrmto, &bnrm, n, &c__1, &beta[1], n, &
		ierr);
    }

    z__1.r = (doublereal) lwkopt, z__1.i = 0.;
    work[1].r = z__1.r, work[1].i = z__1.i;
    return;

/*     End of ZGGEV3 */

} /* zggev3_ */